Due to the moon's gravitational pull, objects at Earth's surface directly under the moon are slightly lighter. This tiny lessening of gravity would also take effect if the moon were on the exact opposite side of the Earth. The Earth and the moon orbit a common point that is not the dead center of the Earth. That point ends up being somewhere in the mantle on the side of the core directly under the moon.
That means that, while someone standing directly under the moon would be very slightly lighter due to the attraction of the moon's gravity, someone standing on the exact opposite side of the Earth would be the same fraction lighter due to being further away from the center of gravity in the Earth-Moon system.
I make that point to ask a question premised upon it. We could increase this by moving the moon closer to Earth. However, eventually, you would reach the Roche limit and tidal stresses would tear the moon apart. However, a black hole wouldn't be torn apart by tidal stresses and could hypothetically orbit within that limit. Could a black hole of the correct mass in geostationary orbit create dual areas of 1G on an otherwise high-gravity world?